Teleparallel equivalent of general relativity and local Lorentz transformation: Revisited

TL;DR

This paper revisits the teleparallel equivalent of general relativity (TEGR), analyzing how local Lorentz transformations introduce extra degrees of freedom that affect conserved charges, and proposes a constraint to eliminate this ambiguity.

Contribution

It demonstrates how an arbitrary function from local Lorentz transformations influences conserved charges and introduces a skew-symmetric tensor to constrain this function.

Findings

The arbitrary Lorentz function affects conserved charge calculations.

A skew-symmetric tensor constraint removes the influence of the arbitrary function.

Explicit tetrad examples illustrate the impact of local Lorentz transformations.

Abstract

It is well known that the field equations of teleparallel theory which is equivalent to general relativity (TEGR) completely agree with the field equation of general relativity (GR). However, TEGR has six extra degrees of freedom which spoil the true physics. These extra degrees are related to the local Lorentz transformation. In this study, we give three different tetrads of flat horizon space-time that depend only on the radial coordinate. One of these tetrads contains an arbitrary function which comes from local Lorentz transformation. We show by explicate calculations that this arbitrary function spoils the calculations of the conserved charges. We formulate {\it a skew-symmetric tensor} whose vanishing value put a constraint on the arbitrary function. This constraint makes the conserved charges are free from the arbitrary function.